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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Rationality of MUMs and 2-functions - Johannes Wal
 cher (Universität Heidelberg)
DTSTART;TZID=Europe/London:20220721T090000
DTEND;TZID=Europe/London:20220721T100000
UID:TALK175652AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/175652
DESCRIPTION:Points of maximal unipotent monodromy in Calabi-Ya
 u moduli space play a central role in mirror symme
 try\, and also harbor some interesting arithmetic.
  In the classic examples\, suitable expansion coef
 ficients of the (all-genus) prepotential (in polyl
 ogarithms) under the mirror map are integers with 
 an enumerative interpretation on the mirror manifo
 ld. This correspondence should be expected to exte
 nd to periods relative to algebraic cycles capturi
 ng the enumerative geometry relative to Lagrangian
  submanifolds. This expectation is challenged\, ho
 wever\, when the mixed degeneration is not defined
  over Q. After musing about compatibility with mir
 ror symmetry\, I will discuss two recent results t
 hat sharpen these questions further: The first is 
 a theorem proven by Felipe M&uuml\;ller which stat
 es that the coefficients of rational 2-functions a
 re necessarily contained in an abelian number fiel
 d. (As defined in the talk\, 2-functions are forma
 l power series whose coefficients satisfy a natura
 l Hodge theoretic supercongruence.) The second are
  examples worked out in collaboration with B&ouml\
 ;nisch\, Klemm\, and van Straten\, of MUMs that ar
 e themselves not defined over Q.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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